Realization of Finite Spectra of Oscillation Characteristics of Linear Homogeneous Differential Equations

Key Points

• The aim is to construct a linear homogeneous differential equation with specific oscillation characteristics from a finite set of nonnegative numbers.
• Develop a linear homogeneous differential equation of order greater than two.
• Ensure the differential equation has continuous coefficients over the nonnegative half-line.
• Match the spectra of characteristic frequencies to the provided nonnegative set.
• Successfully constructed a differential equation that matches the specified set of oscillation characteristics.
• Demonstrated coinciding strong oscillation exponents of signs, zeros, and roots with the finite set.